LMFDB - Dirichlet character orbit 8042.r

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8042, base_ring=CyclotomicField(402)) M = H._module chi = DirichletCharacter(H, M([35])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,8042)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8042$
Conductor:	$4021$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$402$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4021.r	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{201})$
Fixed field:	Number field defined by a degree 402 polynomial (not computed)

First 31 of 132 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8042}(53,\cdot)$	$1$	$1$	$e\left(\frac{161}{201}\right)$	$e\left(\frac{125}{201}\right)$	$-1$	$e\left(\frac{121}{201}\right)$	$e\left(\frac{251}{402}\right)$	$e\left(\frac{2}{67}\right)$	$e\left(\frac{85}{201}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{343}{402}\right)$	$e\left(\frac{121}{402}\right)$
$\chi_{8042}(147,\cdot)$	$1$	$1$	$e\left(\frac{38}{201}\right)$	$e\left(\frac{32}{201}\right)$	$-1$	$e\left(\frac{76}{201}\right)$	$e\left(\frac{53}{402}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{70}{201}\right)$	$e\left(\frac{26}{67}\right)$	$e\left(\frac{247}{402}\right)$	$e\left(\frac{277}{402}\right)$
$\chi_{8042}(153,\cdot)$	$1$	$1$	$e\left(\frac{154}{201}\right)$	$e\left(\frac{172}{201}\right)$	$-1$	$e\left(\frac{107}{201}\right)$	$e\left(\frac{109}{402}\right)$	$e\left(\frac{66}{67}\right)$	$e\left(\frac{125}{201}\right)$	$e\left(\frac{56}{67}\right)$	$e\left(\frac{197}{402}\right)$	$e\left(\frac{107}{402}\right)$
$\chi_{8042}(245,\cdot)$	$1$	$1$	$e\left(\frac{32}{201}\right)$	$e\left(\frac{101}{201}\right)$	$-1$	$e\left(\frac{64}{201}\right)$	$e\left(\frac{161}{402}\right)$	$e\left(\frac{52}{67}\right)$	$e\left(\frac{133}{201}\right)$	$e\left(\frac{36}{67}\right)$	$e\left(\frac{7}{402}\right)$	$e\left(\frac{265}{402}\right)$
$\chi_{8042}(249,\cdot)$	$1$	$1$	$e\left(\frac{100}{201}\right)$	$e\left(\frac{190}{201}\right)$	$-1$	$e\left(\frac{200}{201}\right)$	$e\left(\frac{277}{402}\right)$	$e\left(\frac{62}{67}\right)$	$e\left(\frac{89}{201}\right)$	$e\left(\frac{12}{67}\right)$	$e\left(\frac{47}{402}\right)$	$e\left(\frac{401}{402}\right)$
$\chi_{8042}(251,\cdot)$	$1$	$1$	$e\left(\frac{199}{201}\right)$	$e\left(\frac{157}{201}\right)$	$-1$	$e\left(\frac{197}{201}\right)$	$e\left(\frac{103}{402}\right)$	$e\left(\frac{47}{67}\right)$	$e\left(\frac{155}{201}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{389}{402}\right)$	$e\left(\frac{197}{402}\right)$
$\chi_{8042}(255,\cdot)$	$1$	$1$	$e\left(\frac{148}{201}\right)$	$e\left(\frac{40}{201}\right)$	$-1$	$e\left(\frac{95}{201}\right)$	$e\left(\frac{217}{402}\right)$	$e\left(\frac{6}{67}\right)$	$e\left(\frac{188}{201}\right)$	$e\left(\frac{66}{67}\right)$	$e\left(\frac{359}{402}\right)$	$e\left(\frac{95}{402}\right)$
$\chi_{8042}(287,\cdot)$	$1$	$1$	$e\left(\frac{130}{201}\right)$	$e\left(\frac{46}{201}\right)$	$-1$	$e\left(\frac{59}{201}\right)$	$e\left(\frac{139}{402}\right)$	$e\left(\frac{27}{67}\right)$	$e\left(\frac{176}{201}\right)$	$e\left(\frac{29}{67}\right)$	$e\left(\frac{41}{402}\right)$	$e\left(\frac{59}{402}\right)$
$\chi_{8042}(331,\cdot)$	$1$	$1$	$e\left(\frac{146}{201}\right)$	$e\left(\frac{197}{201}\right)$	$-1$	$e\left(\frac{91}{201}\right)$	$e\left(\frac{119}{402}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{142}{201}\right)$	$e\left(\frac{47}{67}\right)$	$e\left(\frac{145}{402}\right)$	$e\left(\frac{91}{402}\right)$
$\chi_{8042}(341,\cdot)$	$1$	$1$	$e\left(\frac{128}{201}\right)$	$e\left(\frac{2}{201}\right)$	$-1$	$e\left(\frac{55}{201}\right)$	$e\left(\frac{41}{402}\right)$	$e\left(\frac{7}{67}\right)$	$e\left(\frac{130}{201}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{229}{402}\right)$	$e\left(\frac{55}{402}\right)$
$\chi_{8042}(381,\cdot)$	$1$	$1$	$e\left(\frac{92}{201}\right)$	$e\left(\frac{14}{201}\right)$	$-1$	$e\left(\frac{184}{201}\right)$	$e\left(\frac{287}{402}\right)$	$e\left(\frac{49}{67}\right)$	$e\left(\frac{106}{201}\right)$	$e\left(\frac{3}{67}\right)$	$e\left(\frac{397}{402}\right)$	$e\left(\frac{385}{402}\right)$
$\chi_{8042}(415,\cdot)$	$1$	$1$	$e\left(\frac{94}{201}\right)$	$e\left(\frac{58}{201}\right)$	$-1$	$e\left(\frac{188}{201}\right)$	$e\left(\frac{385}{402}\right)$	$e\left(\frac{2}{67}\right)$	$e\left(\frac{152}{201}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{209}{402}\right)$	$e\left(\frac{389}{402}\right)$
$\chi_{8042}(425,\cdot)$	$1$	$1$	$e\left(\frac{142}{201}\right)$	$e\left(\frac{109}{201}\right)$	$-1$	$e\left(\frac{83}{201}\right)$	$e\left(\frac{325}{402}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{50}{201}\right)$	$e\left(\frac{9}{67}\right)$	$e\left(\frac{119}{402}\right)$	$e\left(\frac{83}{402}\right)$
$\chi_{8042}(439,\cdot)$	$1$	$1$	$e\left(\frac{65}{201}\right)$	$e\left(\frac{23}{201}\right)$	$-1$	$e\left(\frac{130}{201}\right)$	$e\left(\frac{371}{402}\right)$	$e\left(\frac{47}{67}\right)$	$e\left(\frac{88}{201}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{121}{402}\right)$	$e\left(\frac{331}{402}\right)$
$\chi_{8042}(543,\cdot)$	$1$	$1$	$e\left(\frac{176}{201}\right)$	$e\left(\frac{53}{201}\right)$	$-1$	$e\left(\frac{151}{201}\right)$	$e\left(\frac{383}{402}\right)$	$e\left(\frac{18}{67}\right)$	$e\left(\frac{28}{201}\right)$	$e\left(\frac{64}{67}\right)$	$e\left(\frac{139}{402}\right)$	$e\left(\frac{151}{402}\right)$
$\chi_{8042}(549,\cdot)$	$1$	$1$	$e\left(\frac{35}{201}\right)$	$e\left(\frac{167}{201}\right)$	$-1$	$e\left(\frac{70}{201}\right)$	$e\left(\frac{107}{402}\right)$	$e\left(\frac{15}{67}\right)$	$e\left(\frac{1}{201}\right)$	$e\left(\frac{31}{67}\right)$	$e\left(\frac{127}{402}\right)$	$e\left(\frac{271}{402}\right)$
$\chi_{8042}(557,\cdot)$	$1$	$1$	$e\left(\frac{68}{201}\right)$	$e\left(\frac{89}{201}\right)$	$-1$	$e\left(\frac{136}{201}\right)$	$e\left(\frac{317}{402}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{157}{201}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{241}{402}\right)$	$e\left(\frac{337}{402}\right)$
$\chi_{8042}(599,\cdot)$	$1$	$1$	$e\left(\frac{13}{201}\right)$	$e\left(\frac{85}{201}\right)$	$-1$	$e\left(\frac{26}{201}\right)$	$e\left(\frac{235}{402}\right)$	$e\left(\frac{63}{67}\right)$	$e\left(\frac{98}{201}\right)$	$e\left(\frac{23}{67}\right)$	$e\left(\frac{185}{402}\right)$	$e\left(\frac{227}{402}\right)$
$\chi_{8042}(635,\cdot)$	$1$	$1$	$e\left(\frac{86}{201}\right)$	$e\left(\frac{83}{201}\right)$	$-1$	$e\left(\frac{172}{201}\right)$	$e\left(\frac{395}{402}\right)$	$e\left(\frac{56}{67}\right)$	$e\left(\frac{169}{201}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{157}{402}\right)$	$e\left(\frac{373}{402}\right)$
$\chi_{8042}(717,\cdot)$	$1$	$1$	$e\left(\frac{107}{201}\right)$	$e\left(\frac{143}{201}\right)$	$-1$	$e\left(\frac{13}{201}\right)$	$e\left(\frac{17}{402}\right)$	$e\left(\frac{65}{67}\right)$	$e\left(\frac{49}{201}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{193}{402}\right)$	$e\left(\frac{13}{402}\right)$
$\chi_{8042}(733,\cdot)$	$1$	$1$	$e\left(\frac{112}{201}\right)$	$e\left(\frac{52}{201}\right)$	$-1$	$e\left(\frac{23}{201}\right)$	$e\left(\frac{61}{402}\right)$	$e\left(\frac{48}{67}\right)$	$e\left(\frac{164}{201}\right)$	$e\left(\frac{59}{67}\right)$	$e\left(\frac{125}{402}\right)$	$e\left(\frac{23}{402}\right)$
$\chi_{8042}(801,\cdot)$	$1$	$1$	$e\left(\frac{2}{201}\right)$	$e\left(\frac{44}{201}\right)$	$-1$	$e\left(\frac{4}{201}\right)$	$e\left(\frac{299}{402}\right)$	$e\left(\frac{20}{67}\right)$	$e\left(\frac{46}{201}\right)$	$e\left(\frac{19}{67}\right)$	$e\left(\frac{13}{402}\right)$	$e\left(\frac{205}{402}\right)$
$\chi_{8042}(841,\cdot)$	$1$	$1$	$e\left(\frac{47}{201}\right)$	$e\left(\frac{29}{201}\right)$	$-1$	$e\left(\frac{94}{201}\right)$	$e\left(\frac{293}{402}\right)$	$e\left(\frac{1}{67}\right)$	$e\left(\frac{76}{201}\right)$	$e\left(\frac{11}{67}\right)$	$e\left(\frac{205}{402}\right)$	$e\left(\frac{295}{402}\right)$
$\chi_{8042}(859,\cdot)$	$1$	$1$	$e\left(\frac{25}{201}\right)$	$e\left(\frac{148}{201}\right)$	$-1$	$e\left(\frac{50}{201}\right)$	$e\left(\frac{19}{402}\right)$	$e\left(\frac{49}{67}\right)$	$e\left(\frac{173}{201}\right)$	$e\left(\frac{3}{67}\right)$	$e\left(\frac{263}{402}\right)$	$e\left(\frac{251}{402}\right)$
$\chi_{8042}(905,\cdot)$	$1$	$1$	$e\left(\frac{170}{201}\right)$	$e\left(\frac{122}{201}\right)$	$-1$	$e\left(\frac{139}{201}\right)$	$e\left(\frac{89}{402}\right)$	$e\left(\frac{25}{67}\right)$	$e\left(\frac{91}{201}\right)$	$e\left(\frac{7}{67}\right)$	$e\left(\frac{301}{402}\right)$	$e\left(\frac{139}{402}\right)$
$\chi_{8042}(915,\cdot)$	$1$	$1$	$e\left(\frac{29}{201}\right)$	$e\left(\frac{35}{201}\right)$	$-1$	$e\left(\frac{58}{201}\right)$	$e\left(\frac{215}{402}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{64}{201}\right)$	$e\left(\frac{41}{67}\right)$	$e\left(\frac{289}{402}\right)$	$e\left(\frac{259}{402}\right)$
$\chi_{8042}(983,\cdot)$	$1$	$1$	$e\left(\frac{110}{201}\right)$	$e\left(\frac{8}{201}\right)$	$-1$	$e\left(\frac{19}{201}\right)$	$e\left(\frac{365}{402}\right)$	$e\left(\frac{28}{67}\right)$	$e\left(\frac{118}{201}\right)$	$e\left(\frac{40}{67}\right)$	$e\left(\frac{313}{402}\right)$	$e\left(\frac{19}{402}\right)$
$\chi_{8042}(1001,\cdot)$	$1$	$1$	$e\left(\frac{61}{201}\right)$	$e\left(\frac{136}{201}\right)$	$-1$	$e\left(\frac{122}{201}\right)$	$e\left(\frac{175}{402}\right)$	$e\left(\frac{7}{67}\right)$	$e\left(\frac{197}{201}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{95}{402}\right)$	$e\left(\frac{323}{402}\right)$
$\chi_{8042}(1195,\cdot)$	$1$	$1$	$e\left(\frac{101}{201}\right)$	$e\left(\frac{11}{201}\right)$	$-1$	$e\left(\frac{1}{201}\right)$	$e\left(\frac{125}{402}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{112}{201}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{355}{402}\right)$	$e\left(\frac{1}{402}\right)$
$\chi_{8042}(1211,\cdot)$	$1$	$1$	$e\left(\frac{194}{201}\right)$	$e\left(\frac{47}{201}\right)$	$-1$	$e\left(\frac{187}{201}\right)$	$e\left(\frac{59}{402}\right)$	$e\left(\frac{64}{67}\right)$	$e\left(\frac{40}{201}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{55}{402}\right)$	$e\left(\frac{187}{402}\right)$
$\chi_{8042}(1259,\cdot)$	$1$	$1$	$e\left(\frac{139}{201}\right)$	$e\left(\frac{43}{201}\right)$	$-1$	$e\left(\frac{77}{201}\right)$	$e\left(\frac{379}{402}\right)$	$e\left(\frac{50}{67}\right)$	$e\left(\frac{182}{201}\right)$	$e\left(\frac{14}{67}\right)$	$e\left(\frac{401}{402}\right)$	$e\left(\frac{77}{402}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8042}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{201}\right)\)	\(e\left(\frac{125}{201}\right)\)	\(-1\)	\(e\left(\frac{121}{201}\right)\)	\(e\left(\frac{251}{402}\right)\)	\(e\left(\frac{2}{67}\right)\)	\(e\left(\frac{85}{201}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{343}{402}\right)\)	\(e\left(\frac{121}{402}\right)\)
\(\chi_{8042}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{201}\right)\)	\(e\left(\frac{32}{201}\right)\)	\(-1\)	\(e\left(\frac{76}{201}\right)\)	\(e\left(\frac{53}{402}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{70}{201}\right)\)	\(e\left(\frac{26}{67}\right)\)	\(e\left(\frac{247}{402}\right)\)	\(e\left(\frac{277}{402}\right)\)
\(\chi_{8042}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{154}{201}\right)\)	\(e\left(\frac{172}{201}\right)\)	\(-1\)	\(e\left(\frac{107}{201}\right)\)	\(e\left(\frac{109}{402}\right)\)	\(e\left(\frac{66}{67}\right)\)	\(e\left(\frac{125}{201}\right)\)	\(e\left(\frac{56}{67}\right)\)	\(e\left(\frac{197}{402}\right)\)	\(e\left(\frac{107}{402}\right)\)
\(\chi_{8042}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{201}\right)\)	\(e\left(\frac{101}{201}\right)\)	\(-1\)	\(e\left(\frac{64}{201}\right)\)	\(e\left(\frac{161}{402}\right)\)	\(e\left(\frac{52}{67}\right)\)	\(e\left(\frac{133}{201}\right)\)	\(e\left(\frac{36}{67}\right)\)	\(e\left(\frac{7}{402}\right)\)	\(e\left(\frac{265}{402}\right)\)
\(\chi_{8042}(249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{100}{201}\right)\)	\(e\left(\frac{190}{201}\right)\)	\(-1\)	\(e\left(\frac{200}{201}\right)\)	\(e\left(\frac{277}{402}\right)\)	\(e\left(\frac{62}{67}\right)\)	\(e\left(\frac{89}{201}\right)\)	\(e\left(\frac{12}{67}\right)\)	\(e\left(\frac{47}{402}\right)\)	\(e\left(\frac{401}{402}\right)\)
\(\chi_{8042}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{201}\right)\)	\(e\left(\frac{157}{201}\right)\)	\(-1\)	\(e\left(\frac{197}{201}\right)\)	\(e\left(\frac{103}{402}\right)\)	\(e\left(\frac{47}{67}\right)\)	\(e\left(\frac{155}{201}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{389}{402}\right)\)	\(e\left(\frac{197}{402}\right)\)
\(\chi_{8042}(255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{201}\right)\)	\(e\left(\frac{40}{201}\right)\)	\(-1\)	\(e\left(\frac{95}{201}\right)\)	\(e\left(\frac{217}{402}\right)\)	\(e\left(\frac{6}{67}\right)\)	\(e\left(\frac{188}{201}\right)\)	\(e\left(\frac{66}{67}\right)\)	\(e\left(\frac{359}{402}\right)\)	\(e\left(\frac{95}{402}\right)\)
\(\chi_{8042}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{201}\right)\)	\(e\left(\frac{46}{201}\right)\)	\(-1\)	\(e\left(\frac{59}{201}\right)\)	\(e\left(\frac{139}{402}\right)\)	\(e\left(\frac{27}{67}\right)\)	\(e\left(\frac{176}{201}\right)\)	\(e\left(\frac{29}{67}\right)\)	\(e\left(\frac{41}{402}\right)\)	\(e\left(\frac{59}{402}\right)\)
\(\chi_{8042}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{201}\right)\)	\(e\left(\frac{197}{201}\right)\)	\(-1\)	\(e\left(\frac{91}{201}\right)\)	\(e\left(\frac{119}{402}\right)\)	\(e\left(\frac{53}{67}\right)\)	\(e\left(\frac{142}{201}\right)\)	\(e\left(\frac{47}{67}\right)\)	\(e\left(\frac{145}{402}\right)\)	\(e\left(\frac{91}{402}\right)\)
\(\chi_{8042}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{128}{201}\right)\)	\(e\left(\frac{2}{201}\right)\)	\(-1\)	\(e\left(\frac{55}{201}\right)\)	\(e\left(\frac{41}{402}\right)\)	\(e\left(\frac{7}{67}\right)\)	\(e\left(\frac{130}{201}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{229}{402}\right)\)	\(e\left(\frac{55}{402}\right)\)
\(\chi_{8042}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{201}\right)\)	\(e\left(\frac{14}{201}\right)\)	\(-1\)	\(e\left(\frac{184}{201}\right)\)	\(e\left(\frac{287}{402}\right)\)	\(e\left(\frac{49}{67}\right)\)	\(e\left(\frac{106}{201}\right)\)	\(e\left(\frac{3}{67}\right)\)	\(e\left(\frac{397}{402}\right)\)	\(e\left(\frac{385}{402}\right)\)
\(\chi_{8042}(415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{201}\right)\)	\(e\left(\frac{58}{201}\right)\)	\(-1\)	\(e\left(\frac{188}{201}\right)\)	\(e\left(\frac{385}{402}\right)\)	\(e\left(\frac{2}{67}\right)\)	\(e\left(\frac{152}{201}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{209}{402}\right)\)	\(e\left(\frac{389}{402}\right)\)
\(\chi_{8042}(425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{142}{201}\right)\)	\(e\left(\frac{109}{201}\right)\)	\(-1\)	\(e\left(\frac{83}{201}\right)\)	\(e\left(\frac{325}{402}\right)\)	\(e\left(\frac{13}{67}\right)\)	\(e\left(\frac{50}{201}\right)\)	\(e\left(\frac{9}{67}\right)\)	\(e\left(\frac{119}{402}\right)\)	\(e\left(\frac{83}{402}\right)\)
\(\chi_{8042}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{201}\right)\)	\(e\left(\frac{23}{201}\right)\)	\(-1\)	\(e\left(\frac{130}{201}\right)\)	\(e\left(\frac{371}{402}\right)\)	\(e\left(\frac{47}{67}\right)\)	\(e\left(\frac{88}{201}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{121}{402}\right)\)	\(e\left(\frac{331}{402}\right)\)
\(\chi_{8042}(543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{176}{201}\right)\)	\(e\left(\frac{53}{201}\right)\)	\(-1\)	\(e\left(\frac{151}{201}\right)\)	\(e\left(\frac{383}{402}\right)\)	\(e\left(\frac{18}{67}\right)\)	\(e\left(\frac{28}{201}\right)\)	\(e\left(\frac{64}{67}\right)\)	\(e\left(\frac{139}{402}\right)\)	\(e\left(\frac{151}{402}\right)\)
\(\chi_{8042}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{201}\right)\)	\(e\left(\frac{167}{201}\right)\)	\(-1\)	\(e\left(\frac{70}{201}\right)\)	\(e\left(\frac{107}{402}\right)\)	\(e\left(\frac{15}{67}\right)\)	\(e\left(\frac{1}{201}\right)\)	\(e\left(\frac{31}{67}\right)\)	\(e\left(\frac{127}{402}\right)\)	\(e\left(\frac{271}{402}\right)\)
\(\chi_{8042}(557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{201}\right)\)	\(e\left(\frac{89}{201}\right)\)	\(-1\)	\(e\left(\frac{136}{201}\right)\)	\(e\left(\frac{317}{402}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{157}{201}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{241}{402}\right)\)	\(e\left(\frac{337}{402}\right)\)
\(\chi_{8042}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{201}\right)\)	\(e\left(\frac{85}{201}\right)\)	\(-1\)	\(e\left(\frac{26}{201}\right)\)	\(e\left(\frac{235}{402}\right)\)	\(e\left(\frac{63}{67}\right)\)	\(e\left(\frac{98}{201}\right)\)	\(e\left(\frac{23}{67}\right)\)	\(e\left(\frac{185}{402}\right)\)	\(e\left(\frac{227}{402}\right)\)
\(\chi_{8042}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{201}\right)\)	\(e\left(\frac{83}{201}\right)\)	\(-1\)	\(e\left(\frac{172}{201}\right)\)	\(e\left(\frac{395}{402}\right)\)	\(e\left(\frac{56}{67}\right)\)	\(e\left(\frac{169}{201}\right)\)	\(e\left(\frac{13}{67}\right)\)	\(e\left(\frac{157}{402}\right)\)	\(e\left(\frac{373}{402}\right)\)
\(\chi_{8042}(717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{201}\right)\)	\(e\left(\frac{143}{201}\right)\)	\(-1\)	\(e\left(\frac{13}{201}\right)\)	\(e\left(\frac{17}{402}\right)\)	\(e\left(\frac{65}{67}\right)\)	\(e\left(\frac{49}{201}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{193}{402}\right)\)	\(e\left(\frac{13}{402}\right)\)
\(\chi_{8042}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{112}{201}\right)\)	\(e\left(\frac{52}{201}\right)\)	\(-1\)	\(e\left(\frac{23}{201}\right)\)	\(e\left(\frac{61}{402}\right)\)	\(e\left(\frac{48}{67}\right)\)	\(e\left(\frac{164}{201}\right)\)	\(e\left(\frac{59}{67}\right)\)	\(e\left(\frac{125}{402}\right)\)	\(e\left(\frac{23}{402}\right)\)
\(\chi_{8042}(801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{201}\right)\)	\(e\left(\frac{44}{201}\right)\)	\(-1\)	\(e\left(\frac{4}{201}\right)\)	\(e\left(\frac{299}{402}\right)\)	\(e\left(\frac{20}{67}\right)\)	\(e\left(\frac{46}{201}\right)\)	\(e\left(\frac{19}{67}\right)\)	\(e\left(\frac{13}{402}\right)\)	\(e\left(\frac{205}{402}\right)\)
\(\chi_{8042}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{201}\right)\)	\(e\left(\frac{29}{201}\right)\)	\(-1\)	\(e\left(\frac{94}{201}\right)\)	\(e\left(\frac{293}{402}\right)\)	\(e\left(\frac{1}{67}\right)\)	\(e\left(\frac{76}{201}\right)\)	\(e\left(\frac{11}{67}\right)\)	\(e\left(\frac{205}{402}\right)\)	\(e\left(\frac{295}{402}\right)\)
\(\chi_{8042}(859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{201}\right)\)	\(e\left(\frac{148}{201}\right)\)	\(-1\)	\(e\left(\frac{50}{201}\right)\)	\(e\left(\frac{19}{402}\right)\)	\(e\left(\frac{49}{67}\right)\)	\(e\left(\frac{173}{201}\right)\)	\(e\left(\frac{3}{67}\right)\)	\(e\left(\frac{263}{402}\right)\)	\(e\left(\frac{251}{402}\right)\)
\(\chi_{8042}(905,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{170}{201}\right)\)	\(e\left(\frac{122}{201}\right)\)	\(-1\)	\(e\left(\frac{139}{201}\right)\)	\(e\left(\frac{89}{402}\right)\)	\(e\left(\frac{25}{67}\right)\)	\(e\left(\frac{91}{201}\right)\)	\(e\left(\frac{7}{67}\right)\)	\(e\left(\frac{301}{402}\right)\)	\(e\left(\frac{139}{402}\right)\)
\(\chi_{8042}(915,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{201}\right)\)	\(e\left(\frac{35}{201}\right)\)	\(-1\)	\(e\left(\frac{58}{201}\right)\)	\(e\left(\frac{215}{402}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{64}{201}\right)\)	\(e\left(\frac{41}{67}\right)\)	\(e\left(\frac{289}{402}\right)\)	\(e\left(\frac{259}{402}\right)\)
\(\chi_{8042}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{110}{201}\right)\)	\(e\left(\frac{8}{201}\right)\)	\(-1\)	\(e\left(\frac{19}{201}\right)\)	\(e\left(\frac{365}{402}\right)\)	\(e\left(\frac{28}{67}\right)\)	\(e\left(\frac{118}{201}\right)\)	\(e\left(\frac{40}{67}\right)\)	\(e\left(\frac{313}{402}\right)\)	\(e\left(\frac{19}{402}\right)\)
\(\chi_{8042}(1001,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{201}\right)\)	\(e\left(\frac{136}{201}\right)\)	\(-1\)	\(e\left(\frac{122}{201}\right)\)	\(e\left(\frac{175}{402}\right)\)	\(e\left(\frac{7}{67}\right)\)	\(e\left(\frac{197}{201}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{95}{402}\right)\)	\(e\left(\frac{323}{402}\right)\)
\(\chi_{8042}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{201}\right)\)	\(e\left(\frac{11}{201}\right)\)	\(-1\)	\(e\left(\frac{1}{201}\right)\)	\(e\left(\frac{125}{402}\right)\)	\(e\left(\frac{5}{67}\right)\)	\(e\left(\frac{112}{201}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{355}{402}\right)\)	\(e\left(\frac{1}{402}\right)\)
\(\chi_{8042}(1211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{194}{201}\right)\)	\(e\left(\frac{47}{201}\right)\)	\(-1\)	\(e\left(\frac{187}{201}\right)\)	\(e\left(\frac{59}{402}\right)\)	\(e\left(\frac{64}{67}\right)\)	\(e\left(\frac{40}{201}\right)\)	\(e\left(\frac{34}{67}\right)\)	\(e\left(\frac{55}{402}\right)\)	\(e\left(\frac{187}{402}\right)\)
\(\chi_{8042}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{201}\right)\)	\(e\left(\frac{43}{201}\right)\)	\(-1\)	\(e\left(\frac{77}{201}\right)\)	\(e\left(\frac{379}{402}\right)\)	\(e\left(\frac{50}{67}\right)\)	\(e\left(\frac{182}{201}\right)\)	\(e\left(\frac{14}{67}\right)\)	\(e\left(\frac{401}{402}\right)\)	\(e\left(\frac{77}{402}\right)\)

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First 31 of 132 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8042.r
Modulus	$8042$
Conductor	$4021$
Order	$402$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8042\)
Conductor:	\(4021\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(402\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4021.r	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)